Irrationality of Our Universe
by September Severtana
Summary: Sherlock has decided John is much like the square root of two: completely irrational. But that doesn't make him love John any less.


**Finally, I went to another lecture at my local college, but this time was about math, so I got really excited to write a Universe oneshot. Anyway, hope you guys enjoy it!**

* * *

Dearest John,

I had never believed in love at first sight.

I know you could be laughing at me for even considering it, but it's true. I didn't believe in love at first sight.

What about now, you'll ask me. Do you believe in it now?

And the truth is, I do.

Yes, yes, the surprised look on your face can be put to rest. Why should the entirely logical man believe in such things? You'll gently make fun of me and then you'll drop it, because somewhere in your head will be questioning. You never ask me what you really want to ask me, and it's rather infuriating, but it doesn't really matter. I'll tell you anyway, just to get it off my chest. Secrets weigh people down, that's what I've learned.

I'll have to start from the beginning, then. That's how it works.

The Greeks seem to be the start of a lot of things, like number theory. I am a scientist, but I think numbers have their own sort of beauty. But at the start, perhaps 500 BC, the Greeks believed the universe was rational and comprehensible through the use of numbers. If a theory could be proven through an airtight process of logic, then it was true forever. They were much like me; logic was the only way to prove things, to understand things. There was simply no comprehension of ideas that couldn't be proven or easily thought through. Existence was numerical, and numbers behaved in certain ways.

My existence was like that, once. All people were the same, the world was an ugly place not meant to hold someone like me: a genius with too much knowledge of his power.

But then, the Greeks discovered what I did over 2500 years later: some don't behave like the others. Some numbers (some people) (one person, really) behaves differently than all the others. What was the square root of two?

Not the rounded off one you use for minor calculations. The _real_ square root of two. Can't tell me? I don't know either. Neither did the Greeks. They had discovered the first irrational number, the one that didn't fit into all their little boxes, into their predetermined notions of the universe. My first irrational number, my first and only square root of two is you, John.

Of course, the Greeks, led by Pythagoras and his band of trail-blazing mathematicians, decided the square root of two had to be rationalized somehow. They started by stating that the exact number had to be between one and two. Well, there are an infinite number of numbers between one and two (a portion of the proof concerning the continuum hypothesis, but that's for another time). Because all the Greeks knew were fractions, they tried multiple ones. 3/2 times 3/2 equals 9/4 or 2.25 which was too much. 5/4 times 5/4 equals 25/16 or 1.5625, but that was too small.

So, because the Greeks were stuck, someone decided that if the square root of two was a fraction, there could be a proof for it. This made all the Pythagoreans happy, and they set out to create a proof. Now, before I show you, there's a bit of mathematical theory you need to know. All fractions can be reduced to simplest form, therefore, there can't be an even number in both the numerator and denominator.

The proof started like this: Square root of two = p/q (standard variable form of a fraction)

Both sides needed to be squared: 2 = p2/q2

Move some things around a bit and you get: p2 = 2q2

According to that proof, 'p' has to be divisible by two. If you do a similar thing except isolating 'q' instead of 'p', the same problem comes up. Both the numerator and the denominator turn out even, which is impossible. The Pythagoreans were extremely baffled by this. Couldn't all numbers be turned into rational fractions?

You see, I did a proof like this of my own. When I first met you, a person, a _species_ that I had never encountered before, I had no idea what you were. You seemed so different from everyone else, not a simple fraction that I could solve and throw behind me. No, you had no decimal equivalent, no rationality. Whenever I tried to figure you out, you changed. I went through reams of paper in my mind palace trying to prove that you were exactly like every single other person I'd met, but I came up empty, just like the Greeks did, until something hit me, just as with them.

Some numbers are irrational. Some figures have no repeating or terminating decimal, or even a whole number. Some numbers, most numbers actually, exist beyond the finite forms of human minds. We simply can't comprehend how far they go. There is no stopping irrational numbers from tearing through everything you once knew was true. Or maybe that just applies to you.

It's chaos out there in that big-small city of London with the big-small world. John, you're all the chaos I need for the rest of my days. You never make sense, but I don't need you to. I have never needed you to make sense to me. Irrationality, when it looks like you, is the best thing to ever happen to me.

You're my favorite paradox, the one equation I can't solve, but I'm alright with that. I've made my peace with irrationality because of one simple irrationality that has taken me over like a conquering emperor, but I'll let you in whenever you ask.

I fell in love with you at first sight, and it's right then that my eyes were opened to how many illogical, nonsensical, wonderful things I had missed without you in my life. For that, I owe you so much. I can never repay you, my beautiful, irrational square root of two. I can never repay you for showing me the world.

With all my love,

William Sherlock Scott Holmes

* * *

John smiles as he notices how happy Sherlock looks today. There hasn't been a case in several days, but there are no new bullet holes in the wall, and a great deal fewer experiments lying around the flat. It doesn't seem like anything's different, though, if you looked at him. That little grin on his face creeped its way over Sherlock's whole body early in the day, and John has no idea why, but he likes it. It's a nice change.

Not very long ago, maybe a couple weeks, Sherlock was stuck in an abysmal slump, barely eating, barely sleeping, playing the violin until John saw his fingers shake. He'd only moved in a few days ago then, so he had no clue as to how he should handle this as Sherlock's flatmate, so he settled for being Sherlock's doctor. He confined Sherlock to bed, made sure he ate, read to him, did stupidly childlike things, but it made Sherlock get better, and now, that smile on his face is making John want to smile too.

He's almost afraid to ask, since Sherlock will probably brush him off. Plus, John never seems to ask the right questions.

"Hey, Sher?"

"Yes, John?" And Sherlock has turned his beaming gaze towards him and it's all John can do not to run up and hug him.

"Any reason for why you're so happy today?"

Sherlock nods. "I've come to a very important conclusion, one that changes my entire view of the world."

"And what may that be?" John sits down and props his chin on his hand, the very picture of a good listener.

Sherlock laughs, and it's a really nice sound. He hasn't laughed in a while, John absently notices.

"I'm in love. I fell in love at first sight, when I never believed such a thing was possible."

Of course, this dampens John's mood quite a bit. "Really? Would I know who?"

"I think you know this person very well." And there's inside-joke laughter in his eyes that John doesn't understand.

"Come on, you've got to give me more than that, Sherlock," John chides, folding his arms. Who on earth would Sherlock, of all people, fall in love with? Who would even be worthy of that? The list has got to be really short.

"Hm," Sherlock muses, but there's a knock at the door before he can say anything. "Yes, it's open."

John seriously wants to strangle whoever it is that would dare come in at such a crucial point in the conversation. It's Lestrade, but that still doesn't quell his desire for murder. He glares at the man the whole time he's there, explaining a new case to Sherlock. Lestrade briefly glances at John, but learns not to based on the look on jOhn's face.

"What's the matter with him?" he asks, after John has gone into the other room to grab his jacket.

Sherlock winks. "You'll find out later. I plan to make this as big of a scene as I can."

* * *

The crime scene is boring, a dead body, stabbed once through the heart, and John can palpably feel the deductions flowing off of Sherlock's skin. He fell in love with someone, John muses. Sherlock Holmes is in love. But with whom?

It's driving John completely mad, but he would rather eat slugs than say it.

"The man is mid-twenties, mathematics major at the local university, has a steady girlfriend, but is having an affair with one of his male classmates. His theorem concerning the continuum hypothesis is in his pocket, so he went to class before he died. His girlfriend doesn't know about the affair, so it couldn't have been her, but it had to have been someone who knew about it," Sherlock rattles off. John loves watching him work. It's amazing, the way he thinks, the way he speaks. "Both in same maths classes, so another friend? Perhaps a male friend?"

It hits John just then. "If the two boys were in the same class, then they would have had the same professor. If that professor disapproved of their relationship and knew about the really good ideas about the continuum hypothesis, he or she could have killed the victim and took the notes as their own."

Sherlock stares at John like the Sun just came up in his eyes. "That's brilliant, John! That is absolutely wonderful, the professor committed the crime! Lestrade!" he yells, and the man comes over to them, and suddenly, John remembers his bad mood. What if the person Sherlock fell in love with is the Detective Inspector? That would make killing him difficult, John huffs to himself.

As soon as Sherlock is done speaking to Lestrade, he shoves the man out of the way and walks right up to John, getting very into his personal space, but John definitely doesn't mind as much as he's supposed to. "My brilliant, beautiful, irrational John." And Sherlock plants his lips on John's. Suddenly, quite a few things are lining up.

The kissing goes on for a few more seconds, and when Sherlock pulls away, John smiles at him. "It was me all along."

"Yeah." Sherlock's grinning too, and John loves it.

"You love me back?"

"You love me in the first place?"

"I never said I didn't."

"You weren't giving very clear signs."

"You never wanted me to."

"I love you, John."

"I love you too, Sherlock."

* * *

 **How was it? The continuum hypothesis stuff was a nod to the other half of the lecture, just so you know. Please read + review!**


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